Certain Domination Parameters and its Resolving Version of Fractal Cubic Networks

TL;DR

This paper studies the domination and resolving domination parameters of fractal cubic networks, a variant of hypercube networks used in supercomputing, revealing their structure as rooted products of graphs and their potential applications.

Contribution

It introduces the analysis of domination parameters for fractal cubic networks, clarifying their structure as rooted products and exploring their applications in resource allocation.

Findings

Fractal cubic networks are rooted products of two graphs.

Domination parameters are characterized for these networks.

Potential applications in resource location and broadcasting.

Abstract

Networks are designed to communicate, operate and allocate the tasks to the respective commodities. Operating the supercomputers became challenging, and it was handled by the network design commonly known as hypercube, denoted by $Q^n$. In a recent study, the hypercube networks were not enough to hold the parallel processors in the supercomputers. Thus, variants of hypercubes were discovered to produce an alternative to the hypercube. A new variant of the hypercube, the \textit{fractal cubic network}, can be used as the best alternative in the case of hypercubes, which was wrongly defined in [Eng. Sci. Technol. \textbf{18}(1) (2015) 32--41]. Arulperumjothi et al. recently corrected this definition and redefined the network in [Appl. Math. Comput. \textbf{452} (2023) 128037]. Our research investigates that the fractal cubic network is a \textit{rooted product} of two graphs. We try to determine its domination and resolving domination parameters, which could be applied to resource location and broadcasting-related problems.